EXPECTED UTILITY OF AN INVESTMENT


Once your utility function is specified, we can calculate the expected utility of an investment. This calculation involves multiplying the utile value of a particular outcome by the probability of its occurrence and adding together the product for all probabilities.

 Illustrations:

Consider two investments that have cashflow streams and assonated probabilities.

 Project A Project B

Cashflows Utiles Prob. Cashflows Utiles Prob.

Sh -20,000 -0.20 0.10 Sh -25,000 -0.25 0.10

0 0 0.10 0 0 0.20

60,000 0.60 0.60 50,000 0.50 0.50

80,000 0.80 0.50 100,000 1.00 0.20

 The expected monetary value for Project A is

 -20,000 (0.10) + 0(0.10) + 60,000 x (0.6) + 80,000 (0.20)

= Shs 50,000

 For Project B

 -25,000 (0.10) + 0 (0.20) + 50,000 (0.50) + 100,000 (0.20)

= Sh 42,500

 Using the expected monetary value, Project A is preferred then Project B.

 Using the utility values (utiles) the expected utility value is computed as follows:

Project A Project B

Utile Prob. Weighted Utile Prob. Weighted

Utility Utility

-0.20 0.10 -0.02 -0.25 0.10 -0.025

0 0.10 0 0 0.20 0

0.60 0.60 0.36 0.50 0.50 0.25

0.80 0.20 0.16 1.00 0.20 0.20

Expect utility value 0.540.425

 Using utility values Project A should be accepted since it has a higher utility value.

 Advantages of utility approach

 1. The risk preferences of the decision maker are directly incorporated in the capital budgeting analysis.

2. It facilitates the process of delegating the authority for decision.

 Limitations

1. It is hard to determine the utility function (it is subjective).

2. The derived utility function is only valid at a point of time.

3. If the decision is taken by a group of people it is hard to determine the utility functions since individuals differ in their risk preferences.